David (Speyer) pointed out an interesting wrinkle that first appears when there are 6 pirates. Recall that the 5 pirate game has the solution that the 5th pirate offers (1, 0, 2, 0, 97) or (0,1,2,0,97) (both are equally good, and by the preferences given there is no way for him to decide). Now the 6th pirate needs to buy off 3 other pirates. Clearly he can buy off pirate 4 for just 1 coin. However, since neither pirate 1 nor 2 knows for sure that he'll be getting 1 coin, he can in fact buy off both of those for 1 coin each. Thus the 6th pirate offers (1,1,0,1,0,97).

On the other hand, if, for example, pirates would rather give money to older pirates than younger ones, then the 5th pirate would always offer (1,0,2,0,0,97), forcing the 6th pirate to offer (2,1,0,1,0,96).

This is when things start getting complicated. Suppose that the 6th pirate does offer (1,1,0,1,0,97). Then pirate 5 has a huge incentive to promise pirate 1 that he'll give him a coin in the next round, and no incentive to ever break that promise. Thus if one's word has even completely negligible value 5 can throw a wrench in the system and convince 1 to vote pirate 6 off the island so to speak. Hence, if one's word has negligible value and the pirates are allowed to make offers, pirate 6 can be forced to offer (2,2,0,1,0,96).